Surveying of Pure and Hybrid Plasmonic Structures Basedon Graphene for Terahertz Antenna

Seyed Ehsan Hosseininejad1,2, Eduard Alarcón2, Nader Komjani1, Sergi Abadal2, MaxC. Lemme3, Peter Haring Bolívar3 and Albert Cabellos-Aparicio2

1Electrical Engineering Department, Iran University of Science and Technology (IUST), Tehran, Iran2NaNoNetworking Center in Catalonia (N3Cat), Universitat Politècnica de Catalunya, Barcelona, Spain3Department of Electrical Engineering and Computer Science, University of Siegen, Siegen, Germany

ABSTRACT

Graphene is a unique material for the implementation ofterahertz antennas due to extraordinary properties of theresulting devices, such as tunability and compactness. Ex-isting graphene antennas are based on pure plasmonic struc-tures, which are compact but show moderate to high losses.To achieve higher efficiency with low cost, one can apply thetheory behind dielectric resonator antennas widely used inmillimeter-wave systems. This paper presents the concept ofhybridization of surface plasmon and dielectric wave modes.Radiation efficiency, reconfigurability, and miniaturizationof antennas built upon this principle are qualitatively dis-cussed and compared with those of pure plasmonic antennas.To this end, a quantitative study of pure and hybrid plas-monic one-dimensional guided-wave structures is performed.The results show that hybrid structures can be employedto design terahertz antennas with high radiation efficiencyand gain, moderate miniaturization, and tunability, whileterahertz antennas based on pure plasmonic structures canprovide high miniaturization and tunability yet with low ra-diation efficiency and gain.

CCS Concepts

•Hardware → Analysis and design of emerging de-vices and systems; Radio frequency and wireless intercon-

nect;

Keywords

Graphene; THz antennas; Plasmonic waveguides; hybridstructures; Surface plasmon waves.

1. INTRODUCTIONGraphene has garnered unprecedented attention due to

its extraordinary properties [1]. The outstanding potential

Corresponding Email: ehsan hosseininejad@elec.iust.ac.ir

Figure 1: The conceptual scheme for hybridizationof surface plasmon and dielectric wave modes to im-plement THz antennas.

of this material opens the door to its application in var-ious fields, including nanometric integrated circuits, spec-troscopy, imaging, transformation optical devices, lenses,modulators, absorbers, directional couplers and metamate-rials, among others [2–8].

Graphene has been also studied in the context of tera-hertz (THz) band communications (0.1 - 10 THz), a keywireless technology enabling a plethora of applications inboth classical networking scenarios, as well as in novel nano-communication paradigms [9–12]. Specifically, graphene hasbeen introduced as an attractive solution for the implemen-tation of miniaturized antennas operating in the terahertzband. Graphene antennas can outperform their metalliccounterparts owing to the unique frequency dispersion ofgraphene and its ability to support Surface Plasmon Po-laritons (SPPs) in this frequency range, where metals actas lossy non-plasmonic conductors [13]. The outstandingproperties of graphene also confer antennas with tunabil-ity, as demonstrated with a novel antenna based on hybridgraphene-metal structure that adds reconfigurability capa-bilities to metallic THz antennas [14].

Dipole-like and patch-like antennas based on the pureplasmonic graphene structures have been investigated in theliterature [15–18]. It has been pointed out that the radiationefficiency of these antennas is low because losses of the sur-face plasmon modes supported by graphene are moderately

(a) 1G (b) 2G

(c) H1G (d) H2G

Figure 2: Geometries of one-dimensional plasmonic waveguides based on graphene including pure plasmonicstructures (a-b) and hybrid structures (c-d).

high at THz frequencies [16, 19]. Instead, hybrid plasmonicguided-wave structures have been introduced to provide abetter balance between mode confinement and propagationloss in the terahertz band [13]. The use of such structurescan lead to the conception of antennas combining the ad-vantages of plasmonics with those of dielectric resonator an-tennas, commonly used in millimeter-wave systems due totheir high miniaturization and gain [20]. Consequently, here,we propose the concept of terahertz antenna based on thehybridization of surface plasmon and dielectric wave modes(Fig. 1).

In the present work, we analyze two types of guided-wavestructures at 3 THz to compare their properties and perfor-mance. First, we consider pure plasmonic structures com-posed by one and two isolated graphene layers. Second, weanalyze hybridized structures that combine the plasmonicmode and dielectric mode. Based on this study of one-dimensional waveguides, we qualitatively discuss three mainfeatures relevant to THz antennas, namely, radiation effi-ciency, tunability, and miniaturization.

The rest of this paper is organized as follows. Section IIpresents the investigation approach and also comparative re-sults of one-dimensional waveguides. In Section III, antennaproperties are evaluated and compared. Finally, conclusionsare provided in Section IV.

2. ONE-DIMENSIONAL STRUCTURES AS

BUILDING BLOCKS OF GRAPHENE AN-

TENNASThe study of guided-wave structures is a basic step for

designing efficient antennas based on those structures. Forexample, consider patch antenna which is a well-known ra-diated-wave device in the microwave frequencies. Knowingthe propagation properties of the microstrip waveguide is

very helpful to design an appropriate patch antenna.Here, an analysis of one-dimensional structures is con-

ducted in order to guide further discussions about the per-formance of antennas based on graphene. Two kinds ofstructures are considered: pure plasmonic structures sup-porting SPP wave modes, and hybrid graphene-dielectricstructures providing coupling of surface plasmons with di-electric waveguide modes. In the first category, a mono-layer graphene structure (1G, Fig. 2(a)) and a structurecomposed of two graphene monolayers separated by thindielectric (2G, Fig. 2(b)) are studied. In the second cat-egory, a hybrid structure with a single graphene monolayer(H1G, Fig. 2(c)) and hybrid structure with two graphenemonolayers (H2G, Fig. 2(d)) are investigated. These hy-brid alternatives include a layer with a high index material(HIM) supporting a dielectric mode, located close to the gra-phene layer supporting a plasmonic mode, but separated bya spacer with a low index material (LIM).

The dimensions and materials employed in each structureare illustrated in Fig. 2. As a primary assumption, GalliumArsenide (GaAs) and polymethylmethacrylate (PMMA) areused for HIM and LIM with dielectric constants of 12.9 and2.4, respectively. Moreover, the dimensions of the structuresare defined as d1 = d2 = d3 = 0.1 µm, d4 = d6 = 0.5 µm,d5 = 15 µm, d7 = 2 µm, and d8 = 9 µm. The frequency ofexcitation is 3 THz.

In this work, graphene is represented as a layer of bulkmaterial with small thickness (dG = 0.5 nm). We can de-fine a volume conductivity for this dG-thick monolayer andthen consider a volume current density. Finally, the equiva-lent permittivity εG is calculated by recasting the Maxwellequation with the assumption of harmonic time dependencee+jωt as

(a) 1G (b) 2G (even mode)

(c) H1G (d) H2G (even mode)

Figure 3: Normal electric fields and effective refractive indices of the evaluated structures.

εG = (+σG−imag

ωdG+ ε0) + j(−

σG−real

ωdG). (1)

The complex conductivity σG can be calculated by thewell-known Kubo formula [21] as

σG =−j

ω − jτ−1

e2kBT

π~2

(

µc

kBT+ 2ln(e

−µc

kBT + 1)+

)

+−j(ω − jτ−1)e2

π~2

∫

∞

0

f(−ε) + f(+ε)

(ω − jτ−1)2 − 4(ε/~)2dε,

(2)

where ω is the radian frequency, e is the electron charge,~ is the reduced Plank constant, kB is the Boltzmann con-stant, T is the temperature (T = 300 K in this paper),µc is the chemical potential, and τ is the electron relax-ation time of graphene (τ = 0.6 ps in this paper). Finally,f(ε) = 1/{1 + exp[(ε− µc)/(kBT )]} is the Fermi-Dirac dis-tribution function.

In order to calculate the complex effective index of guidedmodes in the graphene-integrated structures, the formula-tions of transfer matrix theory provided in [7] are applied.The dispersion relation of Transverse Magnetic (TM) modepropagated in a general multilayer one-dimensional struc-ture is defined as follows:

+j

(

γxSεrS

m11 +γxCεrC

m22

)

=γxS γxCεrSεrC

m12, (3)

where γxC =√

γ2eff − k0εrC , γxS =

√

γ2eff − k0εrS, while

εrC and εrS are the dielectric constants of cover and sub-strate layers, respectively, and mij are the elements of thetotal transfer matrix M as defined in [7]. The zeroes of thisequation, which are the guided mode complex propagationconstants

γeff = k0neff = k0(neff − jkeff ) = βeff − jαeff , (4)

are obtained analytically. The full-wave solver COMSOL[22] is used to verify the results of this method.

It is well known that electromagnetic field profiles of struc-tures help to design efficient antennas and also to identifytheir radiation mechanism. Normal electric field profiles andcomplex effective indices neff of the four waveguides areshown in Fig. 3 for µc = 0.5 eV. It should be noted thatthere are two possible modes for 2G and H2G structures,including even mode, in which the normal electric fields iseven symmetric, and odd mode in which the symmetry isodd. Here, the even mode is preferred because of a muchbetter confinement in comparison with the odd mode. Adetailed comparison among pure and hybrid structures isperformed in the following section.

3. QUALITATIVE DISCUSSION ON GRA-

PHENE ANTENNA PERFORMANCEChoosing from all mentioned structures for the construc-

tion of the antenna can be challenging task, but surveyingthe guided-wave characteristics facilitates it. Even though itis not possible to find the structure that will perfectly fit tothe needs of a given application due to inherent trade-offs,there are some criteria that can be used to find the mostsuitable structure in a particular case. In what follows, wedescribe and discuss three criteria relevant to antenna de-sign, namely, miniaturization, radiation efficiency, and tun-ability. Then, we summarize the outcome of the discussion.

3.1 MiniaturizationNanotechnology is providing a plethora of new tools to

design and manufacture miniaturized devices which are ableto perform different tasks at the micro/nanoscale such ascomputing or data storage [9]. Such devices require wirelesscommunications to expand their limited range through in-formation sharing and coordination. Graphene enables theminiaturization of wireless communication units in generaland of the antennas in particular, due to its ability to sup-port SPP waves in the terahertz frequency range. For giv-ing a good measure of the miniaturization, the mode con-finement should be considered from two directions includingvertical confinement and longitudinal confinement.

Here, the resonant length Lres of dipole-like or patch-likeantennas is evaluated here as a measure of longitudinal con-finement. The resonant length can be written as [23]

Lres = nλeff

2n=1

=λ0

2neff

. (5)

The spatial length Ls describes the vertical extent of thepropagating mode. It can be defined as

Ls =1

Re(γxS)+

N∑

i=1

di +1

Re(γxC)(6)

where di (i = 1, 2, . . . , N) is the thickness of i-th layer andN is number of layers. It is more convenient to express Ls

as normalized to the free space diffraction limit (L0 = λ0/2)where λ0 is the free space wavelength.

Fig. 4 shows the (Lres/λ0 – µc) and (Ls/L0 – µc) plots,useful to compare the structures from the aspect of miniatur-ization in longitudinal and vertical directions, respectively.Considering µc = 0.5 eV, the normalized resonance lengthsof 1G, 2G, H1G, and H2G are 0.05, 0.02, 0.25, and 0.5 andtheir normalized spatial lengths are 0.07, 0.03, 0.75, and0.84, respectively. It is thus concluded that pure plasmonicstructures (1G and 2G) have better confinement in both di-rections than hybrid structures (H1G and H2G).

3.2 Radiation EfficiencyRadiation efficiency is an important factor for any an-

tenna. In terahertz antennas, the efficiency is particularlyconcerning due to the already low efficiency of existing sources[16]. The radiation efficiency er of an antenna can be ex-pressed in terms of radiation resistance Rr and ohmic resis-tance Ro as [23]

er =Rr

Rr +Ro

. (7)

With this fundamental equation, it is straightforward tosee that, for a fixed radiation resistance, the efficiency de-creases as the ohmic resistance increases. This ohmic loss

(a)

(b)

Figure 4: Comparing one-dimensional structuresbased on graphene from aspect of longitudinal andvertical miniaturization using (a) normalized reso-nant length (b) normalized spatial length.

is directly related to the attenuation constants of the modepropagating in the specified structure. A suitable qualita-tive measure of superiority of the structures from the aspectof radiation efficiency is the propagation length. This metricis defined as the distance that a SPP must travel to reduceits electric field intensity to 1/e of its initial value, and ismathematically represented by

Lp =1

k0Im(neff )=

1

Im(γeff)=

1

αeff

. (8)

It is more convenient to represent the propagation lengthin the following normalized form

Lp

λeff

=1

k0Im(neff )

Re(neff )

λ0

. (9)

Consequently, the structures are compared from aspect of

radiation efficiency using the (Lp

λeff– µc) plot in Fig. 5. For

µc = 0.5 eV, the normalized propagation lengths of 1G, 2G,H1G, and H2G are 2.4, 3.4, 16.6, and 188.2, respectively.Note that a structure with a high propagation length is de-sirable. It is thus observed that an antenna based on 1G

Figure 5: Comparing one-dimensional structuresbased on graphene from aspect of radiation effi-ciency using normalized propagation length on a log-arithmic scale.

structure has the lowest radiation efficiency among struc-tures while the implementation of terahertz antennas basedon the hybrid structures are faced with a higher radiationefficiency compared with the pure plasmonic structures.

3.3 TunabilityTunability of terahertz antennas is a desirable feature in

wireless communication at both of the macroscale and mi-cro/nanoscale. One of the extraordinary advantages of gra-phene with respect to other materials is that the chemi-cal potential (Fermi level) can be dynamically modified bychanging the electrostatic voltage applied to the graphenesheet. Since the chemical potential determines the reso-nance frequency of graphene-based antennas [14], this givesantenna engineers an opportunity to design graphene-basedradiated-wave structures that can be reconfigured while inoperation. In order to compare the structures from the as-pect of reconfigurability, (neff – µc) plot is depicted in Fig.6. It is clearly seen that the tunability of 1G and 2G struc-tures is much wider than those of H1G and H2G. The reasonof this result is that the 1G and 2G structures support only apure plasmonic mode which is tunable by changing chemicalpotential, while H1G and H2G structures provide a hybridmode which is a combination of plasmonic and dielectricmodes.

3.4 Summarizing DiscussionThe process of graphene antenna design implies a funda-

mental choice between the different basic structures shownin Fig. 2 or other novel structures. Table 1 summarizesthe properties of the four structures mentioned above. Ingeneral terms, a tradeoff between the different characteris-tics of the structures is observed. Making the right choiceof the basic structures for the desired antenna will generallydepend upon the type of application. Applications heav-ily constrained by the size of the wireless communicationunit, e.g. nanosensor networks [9], may require the use ofpure plasmonic antennas despite of their lower radiation ef-ficiency. In applications such as wireless on-chip commu-nication [10], the choice will be driven by the upper layers,

Figure 6: Comparing one-dimensional waveguidesbased on graphene from aspect of tunability usingeffective index on a logarithmic scale versus chemicalpotential.

Table 1: Comparison the antenna performance usingthe one-dimensional structures (1G, 2G, H1G, andH2G).

Structure 1G 2G H1G H2G(even) (even)

Radiation Efficiency ↓↓ ↓ ↑ ↑↑Miniaturization ↑ ↑↑ ↓ ↓

Tunability ↑↑ ↑↑ ↓ ↓

which may require either very high performance or flexibilitythrough a wide tunability.

Another point concerns the implementation of real an-tennas as three-dimensional structures. Various kinds ofantennas can be conceived using the above mentioned one-dimensional structures. The shape of the antennas and feed-ing structures are two important factors in real antennas af-fecting the radiation properties. Consequently, a deep studyon these parameters would be necessary to design efficientTHz antennas.

It is worthy to note that the results of the basic structureswith respect to the chemical potential of graphene are pre-sented in this paper. Another parameter is relaxation timewhich mainly depends on graphene quality achieved duringthe fabrication process. Its value may have a significant im-pact upon the propagation properties of the guided modesand, therefore, on the radiation performance of the designedantennas.

4. CONCLUSIONSThis paper has surveyed the features of four one-dimen-

sional plasmonic structures that may be employed in thedevelopment of graphene antennas. Results reveal funda-mental tradeoffs between efficiency and miniaturization, andbetween efficiency and tunability. These can be used to steerthe design of appropriate structures for terahertz antennasaccording to the specific application requirements at the ma-croscale or at the nanoscale.

5. ACKNOWLEDGMENTS

This work has been partially funded by the Spanish Min-istry of Economıa y Competitividad under grant PCIN-2015-012.

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